Jeremy Hunt, the culture secretary, will set out his version of events to the Leveson inquiry on Thursday as he fights to save his ministerial career amid a weight of allegations casting doubt on his handling of the BSkyB takeover bid.

The Conservative vowed last month to give "my full record of events" when he faces the judge-led inquiry in a week that has seen a number of fellow cabinet ministers take the stand.

He is also expected to be questioned over whether he explicitly backed the move prior to taking over responsibility for the decision from business secretary Vince Cable.

Hunt, who has received strong backing from David Cameron, told MPs in a statement on 25 April, that he was "totally confident that when I present my evidence, the public will see that I conducted this process with scrupulous fairness throughout".

Hunt made the statement the day after emails released by the Leveson inquiry appeared to reveal inappropriate communication between his department and News Corp and on the day that his special adviser, Adam Smith, quit after conceding that his "activities at times went too far" when correspondence between himself and the News Corporation lobbyist Frédéric Michel emerged.

Since then, both Michel and Smith have appeared before Leveson. Cameron has repeatedly faced down calls for Hunt to resign, including as recently as last week after a draft email surfaced showing that Hunt was privately pushing for the takeover to be allowed before he was appointed to oversee the process.

Labour leader Ed Miliband said in an urgent question to the prime minister last month that Cameron should get Sir Alex Allan, his independent adviser on ministerial interests, to investigate claims that Hunt broke three rules in the ministerial code in relation to his dealings with News Corporation.

But the prime minister insisted at the time that there was no evidence that Hunt had broken the ministerial code and stressed it was best for Hunt to be allowed to give evidence to the Leveson inquiry.

"What we have is a judge-led inquiry, witnesses required to give evidence under oath, full access to papers and records, cross-examination by barristers, all live on television," Cameron told MPs on 30 April. "There is nothing this tough or this rigorous that the civil service or the independent adviser could provide."

He added: "I will not wait until the end of the Leveson Inquiry to take action, if action is needed. If new evidence emerges from the Leveson Inquiry that the ministerial code has been broken, I will either seek the advice of Sir Alex Allan or take action directly."

Cameron defended Hunt again amid fresh Labour calls for his resignation after the inquiry heard in Smith's evidence last week that the culture secretary had written an outspoken memo to Cameron staunchly supporting the £8bn Murdoch bid for BSkyB, a month before he was handed the task of adjudicating on it.

The draft, sent on his private Gmail account to Smith on the afternoon of 19 November 2010 goes much further in explicitly backing the bid than the final, more sanitised draft.

Hunt demands of the bid: "Why are we trying to stop it?" and claims that if ministers do not back the bid, they could end up in the wrong place "politically". Both phrases were removed from the later draft, about which Smith emailed: "Much happier with this version!"

Hunt also goes into considerable detail in the original draft showing that he has already rejected the arguments of the bid's opponents.

It also emerged last week that Hunt exchanged texts with Michel at least four times despite telling parliament he had no unofficial contact with the News Corp lobbyist while he was considering the company's bid for BSkyB.

The culture secretary told the Commons on 25 April: "Throughout the bid process, when I got responsibility for it, the contact that I had with Fred Michel was only at official meetings that were minuted with other people present."

Text messages shown to the Leveson inquiry suggest Hunt had undisclosed conversations with Michel as recently as July last year. Michel told the inquiry that he exchanged "one text every three months" with Hunt over the period.

Cameron continued to stand firmly behind Hunt, insisting that the culture secretary acted "impartially" from the moment he took charge of handling the decision in December 2010 and that what he had said about it previously was not relevant.

The prime minister also said he had no regrets about giving the task to Hunt.

On Wednesday the inquiry heard evidence from Cable, who was stripped of his power to adjudicate on the BSkyB bid in its early stages after he was covertly recorded by Daily Telegraph journalists saying he had "declared war on Murdoch" last December.

Cable said that he believed News Corp were trying to get him stripped off his role by proving political bias, but refused to be intimidated by these veiled threats in his handling of the News Corp/BSkyB deal.